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Two-phase fluid displacement and interfacial instabilities under elastic membranes.

Talal T Al-Housseiny¹, Ivan C Christov, Howard A Stone

¹Department of Chemical and Biological Engineering, Princeton University, Princeton, New Jersey 08544, USA. talal@princeton.edu

Physical Review Letters

|August 6, 2013

Summary

An elastic membrane can suppress viscous fingering during gas-liquid displacement in Hele-Shaw flows. This suppression is due to surface tension effects in the tapered flow geometry, stabilizing the interface.

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Area of Science:

Fluid dynamics
Elasticity
Interface phenomena

Background:

The Saffman-Taylor problem describes viscous fingering during fluid displacement.
Hele-Shaw flows are susceptible to instabilities like viscous fingering.
Elastic boundaries introduce new dynamics to fluid interfaces.

Purpose of the Study:

Investigate the elastic Saffman-Taylor problem with a gas displacing a viscous liquid under an elastic membrane.
Analyze the dynamics of the gas-liquid interface and membrane deformation.
Determine conditions for instability suppression and onset.

Main Methods:

Derivation of interface and membrane dynamics equations.
Analysis of surface tension effects in tapered flow geometry.
Identification of critical conditions for fingering instability.

Main Results:

The elastic boundary can suppress viscous fingering instability.
Surface tension at the gas-liquid interface, due to tapered flow, is the suppression mechanism.
Critical conditions for the onset of fingering were determined.

Conclusions:

Elastic membranes can stabilize Hele-Shaw displacements.
The interplay between elasticity, surface tension, and flow geometry is crucial for interface stability.
This study provides insights into controlling fluid instabilities in elastic systems.